Preheat oven to 500°.
Combine eggs, sugar, flour, cornstarch, and vanilla in a medium mixing bowl; beat until smooth. Add milk, and stir until well blended. Pour mixture into pastry shell; dot with butter, and sprinkle with nutmeg.
Place pie in preheated oven; immediately reduce temperature to 350°. Bake 45 minutes or until a knife inserted in center comes out clean. Cool before slicing.